The notion of precision is founded on the precept of repeatability and is defined as the closeness of agreement between repeated measurements of the same object with the same measurement means. Heretofore, slow expensive often labor intensive and operationally disruptive physical tests, such as materials tests or the xe2x80x9cGrubbs testxe2x80x9d, have been used to estimate the precision of a diverse collection of apparatuses, ranging from belt scales to on-line nuclear analyzers. The xe2x80x9cGrubbs testxe2x80x9d acquires its name from the Grubbs estimators procedure developed by Frank E. Grubbs (1972). Grubbs developed this procedure to fill the void where it was physically impossible to make multiple measurements on the same object with the same measurement means. This application of the Grubbs method presumes the existence of this condition, and necessitates replication of observations by means external to and independent of the first means. The Grubbs estimators method is based on the laws of propagation of error. By making three independent simultaneous measurements on the same physical material, it is possible by appropriate mathematical manipulation of the sums and differences of the associated variances to obtain a valid estimate of the precision of the primary means. Application of the Grubbs estimators procedure to estimation of the precision of an apparatus uses the results of a physical test conducted in such a way as to obtain a series of sets of three independent observations.
Common to apparatuses of this type is a response to some physical, chemical, or other property of an object, said response being comprised of a continuous analog or digital stream of information. Generation of a continuous stream of information for a given time period creates a finite population of data, which is definable by various statistical parameters, such as its mean and variance. It is the repeatability of the estimated population parameters that defines the precision of said apparatuses. An improvement on the Grubbs estimators procedure for estimating the precision of an apparatus is set forth in applicant""s U.S. Pat. No. 5,937,372 wherein the method comprises dividing said stream of information from said apparatus into successive or overlapping pairs and calculating an index of precision therefrom for evaluation against a benchmark such as a standard value, a specification, or a contract requirement. The method set forth in U.S. Pat. No. 5,937,372 is a considerable improvement over application of the Grubbs estimators procedure to the results of a physical test because it avoids the need for conduct of the physical test and can be implemented in real time.
This invention addresses use of methods that belong to the class of statistical procedures known as Bootstrap/Jackknife data resampling methods to obtain estimates of precision of an apparatus for evaluation against a benchmark such as a standard value, a specification, or a contract requirement. The technique originally introduced by M. Quenouille (1949) for estimating the bias of a statistical estimator, was later recognized by J. W. Tukey (1958) as a method that could be extended to construct variance estimators. The technology is very calculation intensive and has advanced rapidly only in the last decade as powerful desktop computers became commonplace.
The Bootstrap/Jackknife data resampling methods, as improvements in the invention set forth in U.S. Pat. No. 5,937,372, offer unique advantages. A dataset of size n, comprised of all the members of a finite population, has 2n-1 non-empty subsets. The method set forth in U.S. Pat. No. 5,937,372 uses two of them. The Jackknife uses n of them and the Bootstrap uses more than n or even all 2n-1 subsets. The use of increasingly more subsets correspondingly improves the estimates of the population parameters and of the estimated index of precision. Since precision is unique to the sampling scheme employed, the Bootstrap/Jackknife data resampling methodology offers the added advantage over current practice that it permits emulation of virtually any desired sampling scheme including stratified random sampling and techniques to take advantage of serial correlation. This capability allows optimization of the sampling scheme to meet precision objectives. The Grubbs test applied to the results of physical samples, because the constraints of mechanical sampling systems, are very restrictive often not permitting a Grubbs test sampling scheme comparable to the sampling schemes that would normally be used in routine daily operations.
This invention using application of the Bootstrap/Jackknife data resampling methodology involves repeated resampling of a dataset (population) defined by a data stream for a selected time interval, or a theoretical distribution fitted to a dataset defined by a data stream for a selected time interval. The average estimated index of precision is calculated from a large number of iterations. The exact number of said iterations is discretionary and can run into thousands for relatively small datasets. Calculations can be done by microprocessor and microprocessor instructions internal to the apparatus or by microprocessor and microprocessor instructions external to the apparatus.
A specific dataset (population) defined by a data stream for a selected time interval is only a part of a universe of said data and as such is incomplete, though comprising all available information, and may exhibit anomalous departures from the distribution that is characteristic of the entire universe for said data. A means for minimizing the effects of said anomalous departures consists of fitting a theoretical distribution to said dataset by using techniques such as the generalized lambda distribution or the generalized bootstrap distribution, and resampling said theoretical distribution. The fitting of a theoretical distribution to a specific dataset adds additional calculations to an already computationally intensive process. Its use therefore would depend on balancing the benefits against said additional computation demands.